A bit of nitpicking. In the very early days of radio, playing phonograph records was often used to fill time. Getting live music to sound right was extremely difficult, since radio stations didn’t have either the rooms or the microphones to handle numerous musicians.
As radio grew and networks formed, sound engineers found ways to create music rooms and stations had more money to spend on hiring bands. Even so, local stations often used recordings for blocks of time or in between sports or news or other unpredictably-timed shows.
Programs that consisted of an announcer playing recordings and talking in between records date back to the mid-1930s, the heyday of big bands.
From Wikipedia:
In 1935, while listeners to New York’s WNEW in New York (now information outlet WBBR) were awaiting developments in the Lindbergh kidnapping, [Martin] Block built his audience by playing records between the Lindbergh news bulletins. This led to his Make Believe Ballroom, which began on February 3, 1935 with Block borrowing both the concept and the title from West Coast disc jockey Al Jarvis, creating the illusion that he was broadcasting from a ballroom with the nation’s top dance bands performing live. He bought some records from a local music shop for the program as the radio station had none. Block purchased five Clyde McCoy records, selecting his “Sugar Blues” for the radio show’s initial theme song.
Because Block was told by the station’s sales staff that nobody would sponsor a radio show playing music, he had to find himself a sponsor. Block lined up a producer of reducing pills called “Retardo”. Within a week of sponsoring the program, the company had over 3,000 responses to the ads on Block’s radio show.
Block’s style of announcing was considerably different than the usual manner of delivery at the time. Instead of speaking in a voice loud enough to be heard in a theater, Block spoke in a normal voice, as if he was having a one-on-one conversation with a listener.
Block’s version of Make Believe Ballroom was a huge hit that lasted for years and even spawned a movie with that title. It was syndicated nationally in 1940, but most big cities had a similar program on a local station.
It’s certainly true that a dj-style music show was just one of many types of programs on any station; devoting the whole day to them wouldn’t come until after WWII. But pretty much every regular radio listener would have understood the concept at any time in radio history.